We develop the mathematical properties of a multifractal analysis of data based on the weak scaling exponent. The advantage of this analysis is that it does not require any a priori global regularity assumption on the analyzed signal, in contrast with the previously used H{\"o}lder or p-exponents. As an illustration, we show that this technique allows one to perform a multifractal analysis of MEG signals, which records electromagnetic brain activity, that was not theoretically valid using the formerly introduced methods based on H{\"o}lder or p-exponents.
@article{arxiv.2503.16892,
title = {Multifractal analysis based on the weak scaling exponent and applications to MEG recordings in neuroscience},
author = {Patrice Abry and Phipippe Ciuciu and Merlin Dumeur and Stéphane Jaffard and Guillaume Saës},
journal= {arXiv preprint arXiv:2503.16892},
year = {2025}
}